The question we were given was (where $^nC_c$ is $n$ choose $c$):
Show, using induction and the fact that $^nC_c + ^nC_{(c+1)} = ~^{(n+1)}C_{(c+1)}$, the "hockey stick theorem": the sum from $k=c$ to $n$ of $^kC_c$ $=~^{(n+1)}C_{(c+1)}$ for all appropriate values of $n$ and $c$.
I had originally thought I got the answer but my professor mentioned in class that $P(0)$ isn't the base case and now I'm completely confused...
For the base case I plugged in $0$ as $n$, and then $0$ as $c$ since $c=0$ is the only appropriate $c$ when $n=0$, and then showed that $^0C_0 =~^1C_1.$
Could someone explain where I went wrong... I'm not sure what other base case there is.